Related papers: Parikh's Theorem: A simple and direct automaton co…
Parikh's Theorem says that the Parikh image of a context-free language is semilinear. We give a short proof of Parikh's Theorem using the formulation of Verma, Seidl, and Schwentick in terms of Presburger arithmetic. The proof relies on an…
We investigate commutative images of languages recognised by register automata and grammars. Semi-linear and rational sets can be naturally extended to this setting by allowing for orbit-finite unions instead of only finite ones. We prove…
Parikh's theorem states that every Context Free Language (CFL) has the same Parikh image as that of a regular language. A finite state automaton accepting such a regular language is called a Parikh-equivalent automaton. In the worst case,…
We prove that the Parikh map of a bounded context-free language is a box spline. Moreover we prove that in this case, such a function is rational.
Parikh's Theorem states that every context-free grammar (CFG) is equivalent to some regular CFG when the ordering of symbols in the words is ignored. The same is not true for the so-called weighted CFGs, which additionally assign a weight…
Parikh's theorem is a fundamental result of the formal language's theory. There had been published many proofs and many papers claimed to provide a simplified proof, but most of them are long and still complicated. We provide the proof that…
Parikh's Theorem is a fundamental result in automata theory with numerous applications in computer science: software verification (e.g. infinite-state verification, string constraints, and theory of arrays), verification of cryptographic…
We consider commutative regular and context-free grammars, or, in other words, Parikh images of regular and context-free languages. By using linear algebra and a branching analog of the classic Euler theorem, we show that, under an…
It has been conjectured that the Parikh (commutative) image of every language over an infinite alphabet recognized by an automaton with registers is defined by a rational expression. This conjecture is known to hold for all languages…
It is well-known that: (i) every context-free language over a singleton terminal alphabet is regular, and (ii) the class of languages that satisfy the Pumping Lemma is a proper super-class of the context-free languages. We show that any…
We investigate the conversion of one-way nondeterministic finite automata and context-free grammars into Parikh equivalent one-way and two-way deterministic finite automata, from a descriptional complexity point of view. We prove that for…
The commutative ambiguity of a context-free grammar G assigns to each Parikh vector v the number of distinct leftmost derivations yielding a word with Parikh vector v. Based on the results on the generalization of Newton's method to…
We show that the Parikh image of the language of an NFA with n states over an alphabet of size k can be described as a finite union of linear sets with at most k generators and total size 2^{O(k^2 log n)}, i.e., polynomial for all fixed k…
We consider Parikh images of languages accepted by non-deterministic finite automata and context-free grammars; in other words, we treat the languages in a commutative way --- we do not care about the order of letters in the accepted word,…
The Bar-Hillel construction is a classic result in formal language theory. It shows, by a simple construction, that the intersection of a context-free language and a regular language is itself context-free. In the construction, the regular…
We show a new and constructive proof of the following language-theoretic result: for every context-free language L, there is a bounded context-free language L' included in L which has the same Parikh (commutative) image as L. Bounded…
Parikh-collinear morphisms have the property that all the Parikh vectors of the images of letters are collinear, i.e., the associated adjacency matrix has rank 1. In the conference DLT-WORDS 2023 we showed that fixed points of…
Valence automata are a generalization of various models of automata with storage. Here, each edge carries, in addition to an input word, an element of a monoid. A computation is considered valid if multiplying the monoid elements on the…
The Parikh finite word automaton model (PA) was introduced and studied by Klaedtke and Ruess in 2003. Here, by means of related models, it is shown that the bounded languages recognized by PA are the same as those recognized by…
We study Parikh automata on finite and infinite words. First we establish some results for Parikh automata on finite words. Following, we present several definitions of Parikh automata on infinite words. We consider the deterministic as…